The cleaning of work stations of textile machines by mobile cleaning devices is well-known. There are various methods according to the aspects of which the cleaning device approaches the individual work stations. For example, EP 0 259 622 B1 describes a method with which the cleaning device moves, beginning at a first work station, from work station to work station, up to the last work station. Once such a work cycle has been completed, the cleaning device begins the next working cycle, either immediately or after a certain waiting time from the front. However, this method does not take into account the fact that the individual work stations become contaminated at different speeds. This may be due to, for example, varying submission materials, a varying number of thread breaks that previously occurred or even only the varying spatial positions of the work stations on the textile machine. Accordingly, however, cleaning at different times is necessary for the individual work stations.